Square-Mean Pseudo Almost Periodic Solutions of Infinite Class in the $α$-Norm under the Light of Measure Theory

Abstract

This work concerns the existence and uniqueness of square-mean pseudo almost periodic solutions of infinite class in the $\alpha$-norm. The results are obtained using analytic semigroup, fractional $\alpha$-power theory and by making use of Banach fixed point theory. As a result, we obtain a generalization of the work of Zabsonre et al. [Partial Differential Equations and Applications: Colloquium in Honor of Hamidou Touré, Springer, 2023] in the deterministic case, without unbounded delay. Our results extend and complement many other important results in the literature. Finally, a concrete example is given to illustrate the application of the main results.